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SYLLABUS

UNIT-I

Probability: Sample Space, Events, Counting Sample Points, Probability of an Event, Additive Rules, Conditional Probability, Independence and the Product Rule, Bayes’ Rule. Random Variables and Probability Distributions: Concept of a Random Variable, Discrete Probability Distributions, Continuous Probability Distributions, Statistical Independence.

UNIT-II

Mathematical Expectation: Mean of a Random Variable, Variance and Covariance of Random Variables, Means and Variances of Linear Combinations of Random Variables, Chebyshev’s Theorem. Discrete Probability Distributions: Introduction and Motivation, Binomial Distribution, Geometric Distributions and Poisson Distribution.

UNIT-III

Continuous Probability Distributions: Continuous Uniform Distribution, Normal Distribution, Areas Under the Normal Curve, Applications of the Normal Distribution, Normal Approximation to the Binomial, Gamma and Exponential Distributions. Fundamental Sampling Distributions: Random Sampling, Some Important Statistics, Sampling Distributions, Sampling Distribution of Means and the Central Limit Theorem, Sampling Distribution of S2 , t-Distribution, F-Distribution.

UNIT-IV

Estimation and Tests of Hypotheses: Introduction, Statistical Inference, Classical Methods of Estimation: Estimating the Mean, Standard Error of a Point Estimate, Prediction Intervals, Tolerance Limits, Estimating the Variance, Estimating a Proportion for Single Mean, Difference Between Two Means, Between Two Proportions for Two Samples and Maximum Likelihood Estimation. Statistical Hypotheses: General Concepts, Testing a Statistical Hypothesis, Tests Concerning a Single Mean, Tests on Two Means, Test on a Single Proportion, Two Samples: Tests on Two Proportions.

UNIT-V

Stochastic Processes and Markov Chains: Introduction to Stochastic Processes – Markov Process. Transition Probability, Transition Probability Matrix, First Order and Higher Order Markov Process, n-step Transition Probabilities, Markov Chain, Steady State Condition, Markov Analysis.